Remez algorithm. More...

#include <remez_gmp.h>

Public Member Functions
	RemezGMP ()
	Default constructor. More...

	RemezGMP (const Real &lower, const Real &upper, long prec)
	Constructor. More...

	~RemezGMP ()
	Destructor. More...

void	setBounds (const Real &lower, const Real &upper)
	Reset the bounds of the approximation. More...

Real	generateApprox (int num_degree, int den_degree, unsigned long power_num, unsigned long power_den)
	Generate the rational approximation x^(pnum/pden) More...

Real	generateApprox (int degree, unsigned long power_num, unsigned long power_den)

RemezCoeff_t	getPFE ()
	Return the partial fraction expansion of the approximation x^(pnum/pden) More...

RemezCoeff_t	getIPFE ()
	Return the partial fraction expansion of the approximation x^(-pnum/pden) More...

Real	evalPFE (const Real &x, const RemezCoeff_t &coeff)
	Given a partial fraction expansion, evaluate it at x. More...

Private Member Functions
void	initialGuess ()
	Initial values of maximal and minmal errors. More...

void	equations ()
	Solve the equations. More...

void	search (multi1d< bigfloat > &step)
	Search for error maxima and minima. More...

void	stpini (multi1d< bigfloat > &step)
	Initialise step sizes. More...

int	root ()
	Calculate the roots of the approximation. More...

bigfloat	polyEval (const bigfloat &x, const multi1d< bigfloat > &poly, long size)
	Evaluate the polynomial. More...

bigfloat	polyDiff (const bigfloat &x, const multi1d< bigfloat > &poly, long size)
	Evaluate the differential of the polynomial. More...

bigfloat	rtnewt (const multi1d< bigfloat > &poly, long i, const bigfloat &x1, const bigfloat &x2, const bigfloat &xacc)
	Newton's method to calculate roots. More...

void	pfe (multi1d< bigfloat > &res, multi1d< bigfloat > &poles, const bigfloat &norm)

bigfloat	approx (const bigfloat &x)

bigfloat	func (const bigfloat &x)
	Calculate function required for the approximation. More...

bigfloat	getErr (const bigfloat &x, int &sign)
	Compute size and sign of the approximation error at x. More...

int	simq (multi1d< bigfloat > &A, multi1d< bigfloat > &B, multi1d< bigfloat > &X, int n)
	Solve the system AX=B. More...

void	allocate (int num_degree, int den_degree)
	Free memory and reallocate as necessary. More...

Private Attributes
multi1d< bigfloat >	param

multi1d< bigfloat >	roots

multi1d< bigfloat >	poles

bigfloat	norm

int	n
	The numerator and denominator degree (n=d) More...

int	d

bigfloat	apstrt
	The bounds of the approximation. More...

bigfloat	apwidt

bigfloat	apend

unsigned long	power_num
	the numerator and denominator of the power we are approximating More...

unsigned long	power_den

bool	alloc
	Flag to determine whether the arrays have been allocated. More...

int	nd1
	Variables used to calculate the approximation. More...

int	iter

multi1d< bigfloat >	xx

multi1d< bigfloat >	mm

multi1d< bigfloat >	step

bigfloat	delta

bigfloat	spread

bigfloat	tolerance

int	neq
	The number of equations we must solve at each iteration (n+d+1) More...

long	prec
	The precision of the GNU MP library. More...

Detailed Description

Remez algorithm.

The Remez algorithm is used for generating the nth root rational approximation.

Note this class can only be used if the gnu multiprecision (GNU MP) library is present.

Definition at line 26 of file remez_gmp.h.

Constructor & Destructor Documentation

◆ RemezGMP() [1/2]

Chroma::RemezGMP::RemezGMP ( )

Default constructor.

Definition at line 13 of file remez_gmp.cc.

References alloc, Chroma::END_CODE(), and Chroma::START_CODE().

◆ RemezGMP() [2/2]

Chroma::RemezGMP::RemezGMP	(	const Real &	lower,
		const Real &	upper,
		long	prec
	)

Constructor.

Definition at line 24 of file remez_gmp.cc.

References alloc, apend, apstrt, apwidt, d, Chroma::END_CODE(), n, prec, Chroma::bigfloat::setDefaultPrecision(), Chroma::START_CODE(), and tolerance.

◆ ~RemezGMP()

Chroma::RemezGMP::~RemezGMP ( )

inline

Destructor.

Definition at line 36 of file remez_gmp.h.

Member Function Documentation

◆ allocate()

void Chroma::RemezGMP::allocate	(	int	num_degree,
		int	den_degree
	)

private

Free memory and reallocate as necessary.

Definition at line 54 of file remez_gmp.cc.

References alloc, Chroma::END_CODE(), mm, param, poles, roots, Chroma::START_CODE(), and xx.

Referenced by generateApprox().

◆ approx()

bigfloat Chroma::RemezGMP::approx ( const bigfloat & x )

private

Definition at line 410 of file remez_gmp.cc.

References d, Chroma::END_CODE(), Chroma::i, n, param, Chroma::START_CODE(), and x.

Referenced by getErr().

◆ equations()

void Chroma::RemezGMP::equations ( void )

private

Solve the equations.

Definition at line 367 of file remez_gmp.cc.

References d, Chroma::END_CODE(), func(), Chroma::i, j, n, neq, param, simq(), Chroma::START_CODE(), x, xx, y, and z.

Referenced by generateApprox().

◆ evalPFE()

Real Chroma::RemezGMP::evalPFE	(	const Real &	x,
		const RemezCoeff_t &	coeff
	)

Given a partial fraction expansion, evaluate it at x.

Definition at line 762 of file remez_gmp.cc.

References Chroma::i, Chroma::RemezCoeff_t::norm, Chroma::RemezCoeff_t::pole, Chroma::RemezCoeff_t::res, and x.

◆ func()

bigfloat Chroma::RemezGMP::func ( const bigfloat & x )

private

Calculate function required for the approximation.

Definition at line 447 of file remez_gmp.cc.

References Chroma::END_CODE(), power_den, power_num, prec, Chroma::START_CODE(), x, and y.

Referenced by equations(), and getErr().

◆ generateApprox() [1/2]

Real Chroma::RemezGMP::generateApprox	(	int	degree,
		unsigned long	power_num,
		unsigned long	power_den
	)

Definition at line 83 of file remez_gmp.cc.

References generateApprox().

◆ generateApprox() [2/2]

Real Chroma::RemezGMP::generateApprox	(	int	num_degree,
		int	den_degree,
		unsigned long	power_num,
		unsigned long	power_den
	)

Generate the rational approximation x^(pnum/pden)

Definition at line 89 of file remez_gmp.cc.

References allocate(), d, delta, Chroma::END_CODE(), equations(), getErr(), initialGuess(), iter, mm, n, neq, power_den, power_num, root(), search(), spread, Chroma::START_CODE(), step, stpini(), and tolerance.

Referenced by generateApprox().

◆ getErr()

bigfloat Chroma::RemezGMP::getErr	(	const bigfloat &	x,
		int &	sign
	)

private

Compute size and sign of the approximation error at x.

Definition at line 429 of file remez_gmp.cc.

References approx(), func(), and x.

Referenced by generateApprox(), and search().

◆ getIPFE()

RemezCoeff_t Chroma::RemezGMP::getIPFE ( )

Return the partial fraction expansion of the approximation x^(-pnum/pden)

Definition at line 189 of file remez_gmp.cc.

References alloc, d, Chroma::END_CODE(), Chroma::i, n, Chroma::RemezCoeff_t::norm, norm, Chroma::p, pfe(), Chroma::RemezCoeff_t::pole, poles, Chroma::r, Chroma::RemezCoeff_t::res, roots, and Chroma::START_CODE().

◆ getPFE()

RemezCoeff_t Chroma::RemezGMP::getPFE ( )

Return the partial fraction expansion of the approximation x^(pnum/pden)

Definition at line 149 of file remez_gmp.cc.

References alloc, d, Chroma::END_CODE(), Chroma::i, n, Chroma::RemezCoeff_t::norm, norm, Chroma::p, pfe(), Chroma::RemezCoeff_t::pole, poles, Chroma::r, Chroma::RemezCoeff_t::res, roots, and Chroma::START_CODE().

◆ initialGuess()

void Chroma::RemezGMP::initialGuess ( )

private

Initial values of maximal and minmal errors.

Definition at line 228 of file remez_gmp.cc.

References Chroma::a, apend, apstrt, apwidt, Chroma::END_CODE(), Chroma::i, M_PI, mm, neq, Chroma::r, Chroma::START_CODE(), and xx.

Referenced by generateApprox().

◆ pfe()

void Chroma::RemezGMP::pfe	(	multi1d< bigfloat > &	res,
		multi1d< bigfloat > &	poles,
		const bigfloat &	norm
	)

private

Definition at line 683 of file remez_gmp.cc.

References d, Chroma::END_CODE(), Chroma::i, j, l, n, norm, poles, Chroma::QDP_error_exit(), and Chroma::START_CODE().

Referenced by getIPFE(), and getPFE().

◆ polyDiff()

bigfloat Chroma::RemezGMP::polyDiff	(	const bigfloat &	x,
		const multi1d< bigfloat > &	poly,
		long	size
	)

private

Evaluate the differential of the polynomial.

Definition at line 646 of file remez_gmp.cc.

References Chroma::i, and x.

Referenced by rtnewt().

◆ polyEval()

bigfloat Chroma::RemezGMP::polyEval	(	const bigfloat &	x,
		const multi1d< bigfloat > &	poly,
		long	size
	)

private

Evaluate the polynomial.

Definition at line 638 of file remez_gmp.cc.

References Chroma::i, and x.

Referenced by rtnewt().

◆ root()

int Chroma::RemezGMP::root ( )

private

Calculate the roots of the approximation.

Definition at line 588 of file remez_gmp.cc.

References d, Chroma::END_CODE(), Chroma::i, j, n, neq, norm, param, poles, roots, rtnewt(), Chroma::START_CODE(), and x.

Referenced by generateApprox().

◆ rtnewt()

bigfloat Chroma::RemezGMP::rtnewt	(	const multi1d< bigfloat > &	poly,
		long	i,
		const bigfloat &	x1,
		const bigfloat &	x2,
		const bigfloat &	xacc
	)

private

Newton's method to calculate roots.

Definition at line 655 of file remez_gmp.cc.

References Chroma::END_CODE(), Chroma::i, j, JMAX, polyDiff(), polyEval(), and Chroma::START_CODE().

Referenced by root().

◆ search()

void Chroma::RemezGMP::search ( multi1d< bigfloat > & step )

private

Search for error maxima and minima.

Definition at line 277 of file remez_gmp.cc.

References Chroma::a, apend, apstrt, delta, Chroma::END_CODE(), getErr(), Chroma::i, j, l, mm, neq, q, Chroma::QDP_error_exit(), spread, Chroma::START_CODE(), step, and xx.

Referenced by generateApprox().

◆ setBounds()

void Chroma::RemezGMP::setBounds	(	const Real &	lower,
		const Real &	upper
	)

Reset the bounds of the approximation.

Definition at line 71 of file remez_gmp.cc.

References apend, apstrt, apwidt, Chroma::END_CODE(), and Chroma::START_CODE().

◆ simq()

int Chroma::RemezGMP::simq	(	multi1d< bigfloat > &	A,
		multi1d< bigfloat > &	B,
		multi1d< bigfloat > &	X,
		int	n
	)

private

Solve the system AX=B.

Definition at line 468 of file remez_gmp.cc.

References Chroma::A(), Chroma::END_CODE(), Chroma::i, j, Chroma::k, l, n, neq, q, Chroma::QDP_error_exit(), Chroma::START_CODE(), and sum.

Referenced by equations().

◆ stpini()

void Chroma::RemezGMP::stpini ( multi1d< bigfloat > & step )

private

Initialise step sizes.

Definition at line 260 of file remez_gmp.cc.

References apend, apstrt, delta, Chroma::END_CODE(), Chroma::i, neq, Chroma::QDP_error_exit(), Chroma::START_CODE(), step, and xx.

Referenced by generateApprox().

Member Data Documentation

◆ alloc

bool Chroma::RemezGMP::alloc

private

Flag to determine whether the arrays have been allocated.

Definition at line 72 of file remez_gmp.h.

Referenced by allocate(), getIPFE(), getPFE(), and RemezGMP().

◆ apend

bigfloat Chroma::RemezGMP::apend

private

Definition at line 65 of file remez_gmp.h.

Referenced by initialGuess(), RemezGMP(), search(), setBounds(), and stpini().

◆ apstrt

bigfloat Chroma::RemezGMP::apstrt

private

The bounds of the approximation.

Definition at line 65 of file remez_gmp.h.

Referenced by initialGuess(), RemezGMP(), search(), setBounds(), and stpini().

◆ apwidt

bigfloat Chroma::RemezGMP::apwidt

private

Definition at line 65 of file remez_gmp.h.

Referenced by initialGuess(), RemezGMP(), and setBounds().

◆ d

int Chroma::RemezGMP::d

private

Definition at line 62 of file remez_gmp.h.

Referenced by approx(), equations(), generateApprox(), getIPFE(), getPFE(), pfe(), RemezGMP(), and root().

◆ delta

bigfloat Chroma::RemezGMP::delta

private

Definition at line 77 of file remez_gmp.h.

Referenced by generateApprox(), search(), and stpini().

◆ iter

int Chroma::RemezGMP::iter

private

Definition at line 75 of file remez_gmp.h.

Referenced by generateApprox().

◆ mm

multi1d<bigfloat> Chroma::RemezGMP::mm

private

Definition at line 76 of file remez_gmp.h.

Referenced by allocate(), generateApprox(), initialGuess(), and search().

◆ n

int Chroma::RemezGMP::n

private

The numerator and denominator degree (n=d)

Definition at line 62 of file remez_gmp.h.

Referenced by approx(), equations(), generateApprox(), getIPFE(), getPFE(), pfe(), RemezGMP(), root(), and simq().

◆ nd1

int Chroma::RemezGMP::nd1

private

Variables used to calculate the approximation.

Definition at line 75 of file remez_gmp.h.

◆ neq

int Chroma::RemezGMP::neq

private

The number of equations we must solve at each iteration (n+d+1)

Definition at line 80 of file remez_gmp.h.

Referenced by equations(), generateApprox(), initialGuess(), root(), search(), simq(), and stpini().

◆ norm

bigfloat Chroma::RemezGMP::norm

private

Definition at line 59 of file remez_gmp.h.

Referenced by getIPFE(), getPFE(), pfe(), and root().

◆ param

multi1d<bigfloat> Chroma::RemezGMP::param

private

Definition at line 58 of file remez_gmp.h.

Referenced by allocate(), approx(), equations(), and root().

◆ poles

multi1d<bigfloat> Chroma::RemezGMP::poles

private

Definition at line 58 of file remez_gmp.h.

Referenced by allocate(), getIPFE(), getPFE(), pfe(), and root().

◆ power_den

unsigned long Chroma::RemezGMP::power_den

private

Definition at line 69 of file remez_gmp.h.

Referenced by func(), and generateApprox().

◆ power_num

unsigned long Chroma::RemezGMP::power_num

private

the numerator and denominator of the power we are approximating

Definition at line 68 of file remez_gmp.h.

Referenced by func(), and generateApprox().

◆ prec

long Chroma::RemezGMP::prec

private

The precision of the GNU MP library.

Definition at line 83 of file remez_gmp.h.

Referenced by func(), and RemezGMP().

◆ roots

multi1d<bigfloat> Chroma::RemezGMP::roots

private

Definition at line 58 of file remez_gmp.h.

Referenced by allocate(), getIPFE(), getPFE(), and root().

◆ spread

bigfloat Chroma::RemezGMP::spread

private

Definition at line 77 of file remez_gmp.h.

Referenced by generateApprox(), and search().

◆ step

multi1d<bigfloat> Chroma::RemezGMP::step

private

Definition at line 76 of file remez_gmp.h.

Referenced by generateApprox(), search(), and stpini().

◆ tolerance

bigfloat Chroma::RemezGMP::tolerance

private

Definition at line 77 of file remez_gmp.h.

Referenced by generateApprox(), and RemezGMP().

◆ xx

multi1d<bigfloat> Chroma::RemezGMP::xx

private

Definition at line 76 of file remez_gmp.h.

Referenced by allocate(), equations(), initialGuess(), search(), and stpini().

The documentation for this class was generated from the following files:

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ RemezGMP() [1/2]

◆ RemezGMP() [2/2]

◆ ~RemezGMP()

Member Function Documentation

◆ allocate()

◆ approx()

◆ equations()

◆ evalPFE()

◆ func()

◆ generateApprox() [1/2]

◆ generateApprox() [2/2]

◆ getErr()

◆ getIPFE()

◆ getPFE()

◆ initialGuess()

◆ pfe()

◆ polyDiff()

◆ polyEval()

◆ root()

◆ rtnewt()

◆ search()

◆ setBounds()

◆ simq()

◆ stpini()

Member Data Documentation

◆ alloc

◆ apend

◆ apstrt

◆ apwidt

◆ d

◆ delta

◆ iter

◆ mm

◆ n

◆ nd1

◆ neq

◆ norm

◆ param

◆ poles

◆ power_den

◆ power_num

◆ prec

◆ roots

◆ spread

◆ step

◆ tolerance

◆ xx